What is a Decreasing Interval? | Simple Explanation for Class 9

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What is a Decreasing Interval on a Graph?

Grade Level:

Class 9

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

A decreasing interval on a graph is a section of the graph where the line or curve is going downwards as you move from left to right. This means that as the x-values (input) increase, the y-values (output) decrease.

Simple Example

Quick Example

Imagine you are tracking the price of a kilo of onions at your local sabzi mandi over a week. If the price started at Rs 40 on Monday and dropped to Rs 35 on Wednesday, then the interval from Monday to Wednesday shows a decreasing trend in onion prices.

Worked Example

Step-by-Step

Let's look at the daily temperature in a city over a few hours. Suppose the temperatures are:
Time (x-axis): 1 PM, 2 PM, 3 PM, 4 PM, 5 PM
Temperature (y-axis): 35°C, 33°C, 30°C, 28°C, 29°C

Step 1: Plot these points on a graph. Time is on the horizontal axis, and temperature is on the vertical axis.
---Step 2: Connect the points to see the trend. From 1 PM to 2 PM, the temperature goes from 35°C to 33°C (decreasing).
---Step 3: From 2 PM to 3 PM, it goes from 33°C to 30°C (decreasing).
---Step 4: From 3 PM to 4 PM, it goes from 30°C to 28°C (decreasing).
---Step 5: From 4 PM to 5 PM, it goes from 28°C to 29°C (increasing).
---Step 6: Identify the intervals where the temperature is going down.
Answer: The temperature is decreasing in the interval from 1 PM to 4 PM.

Why It Matters

Understanding decreasing intervals is crucial in fields like Data Science and Economics to spot negative trends, such as a company's sales falling or the stock market dropping. In Physics, it helps analyze when the speed of a moving object is reducing. These skills are vital for careers like financial analysts, data scientists, and engineers.

Common Mistakes

MISTAKE: Confusing decreasing with increasing intervals, especially when the graph line is flat. | CORRECTION: Remember, a decreasing interval means the y-value MUST go down as x goes right. A flat line is a constant interval, not decreasing.

MISTAKE: Only looking at the start and end points of the graph, not the specific sections. | CORRECTION: Always analyze the graph segment by segment. A graph can decrease, then increase, then decrease again. Each segment is a separate interval.

MISTAKE: Saying the graph is decreasing when it's just going left to right downwards, even if the numbers on the x-axis are decreasing. | CORRECTION: Always read a graph from left to right (increasing x-values). If the y-values go down during this left-to-right movement, then it's a decreasing interval.

Practice Questions

Try It Yourself

QUESTION: A graph shows the battery percentage of a phone over time. If the battery goes from 100% at 8 AM to 70% at 10 AM, is this a decreasing interval? | ANSWER: Yes, because as time (x-axis) increases, the battery percentage (y-axis) decreases.

QUESTION: Look at the points (1, 10), (2, 8), (3, 8), (4, 5). Identify the decreasing intervals based on x-values. | ANSWER: The graph is decreasing from x=1 to x=2 (y goes from 10 to 8) and from x=3 to x=4 (y goes from 8 to 5). The interval from x=2 to x=3 is constant.

QUESTION: A graph represents the number of daily active users for a new app. On Monday, there were 500 users. On Tuesday, 480. On Wednesday, 450. On Thursday, 460. On Friday, 470. On which day(s) did the number of users show a decreasing trend from the previous day? | ANSWER: Tuesday (from 500 to 480) and Wednesday (from 480 to 450).

MCQ

Quick Quiz

Which of the following scenarios represents a decreasing interval on a graph?

The number of students in a class remains the same for a month.

The temperature rises from 25°C to 30°C.

The amount of water in a tank reduces from 500 litres to 400 litres over an hour.

The speed of a train stays at 60 km/h for 30 minutes.

The Correct Answer Is:

Option C shows a decrease in the amount of water over time. As time increases, the water level decreases, which is the definition of a decreasing interval. The other options show constant or increasing values.

Real World Connection

In the Real World

Many apps like Google Maps show traffic density. If you see a section of a road where the average speed of vehicles is dropping over time (e.g., from 40 km/h to 10 km/h), that segment of the graph representing speed vs. time for that road shows a decreasing interval. This helps you avoid traffic jams!

Key Vocabulary

Key Terms

INTERVAL: A specific section or range of values on a graph | X-AXIS: The horizontal line on a graph, usually representing the independent variable (like time) | Y-AXIS: The vertical line on a graph, usually representing the dependent variable (like temperature or quantity) | TREND: The general direction or pattern of change in data over time.

What's Next

What to Learn Next

Now that you understand decreasing intervals, you should explore 'Increasing Intervals' and 'Constant Intervals' on a graph. These concepts are closely related and will help you fully describe the behavior of any graph you encounter, which is key for understanding functions.